全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

Frequency-Dependent Streaming Potential of Porous Media—Part 2: Experimental Measurement of Unconsolidated Materials

DOI: 10.1155/2012/728495

Full-Text   Cite this paper   Add to My Lib

Abstract:

Frequency-dependent streaming potential coefficient measurements have been made upon Ottawa sand and glass bead packs using a new apparatus that is based on an electromagnetic drive. The apparatus operates in the range 1?Hz to 1?kHz with samples of 25.4?mm diameter up to 150?mm long. The results have been analysed using theoretical models that are either (i) based upon vibrational mechanics, (ii) treat the geological material as a bundle of capillary tubes, or (iii) treat the material as a porous medium. The best fit was provided by the Pride model and its simplification, which is satisfying as this model was conceived for porous media rather than capillary tube bundles. Values for the transition frequency were derived from each of the models for each sample and were found to be in good agreement with those expected from the independently measured effective pore radius of each material. The fit to the Pride model for all four samples was also found to be consistent with the independently measured steady-state permeability, while the value of the streaming potential coefficient in the low-frequency limit was found to be in good agreement with other steady-state streaming potential coefficient data. 1. Introduction There have only been 10 measurements of the frequency-dependent streaming potential coefficient of porous geological and engineering materials. A review of the existing measurements was carried out by Glover et al. [1]. These previous measurements can be divided into two groups: (i) transient measurements with a percussive source and (ii) harmonic measurements with a vibrating source. While the first of these approaches mimics many of the possible applications more closely [2–4], it cannot provide the streaming potential coupling coefficient as a function of frequency without using the frequency domain filtering and Fourier techniques. Such techniques can only be used in a linear system. Although the equations that describe the streaming potential coefficient are linear below the transition frequency and there is no evidence that they become non-linear above that frequency, it has not yet been shown that such an approach can be made to work for streaming potential coupling coefficient measurements on rocks. The processing of such data has, however, been discussed at length in Reppert and Morgan [5]; they mention that inertial effects may be seen if the transient signal has strong enough high-frequency components. The second approach is capable of providing the streaming potential coupling coefficient at each frequency directly. Its disadvantage

References

[1]  P. W. J. Glover, J. Ruel, and E. Tardif, “Frequency-dependent streaming potential of porous media: 1. Experimental approaches and apparatus design,” International Journal of Geophysics. In press.
[2]  C. Bordes, L. Jouniaux, S. Garambois, M. Dietrich, J. P. Pozzi, and S. Gaffet, “Evidence of the theoretically predicted seismo-magnetic conversion,” Geophysical Journal International, vol. 174, no. 2, pp. 489–504, 2008.
[3]  C. Bordes, L. Jouniaux, M. Dietrich, J. P. Pozzi, and S. Garambois, “First laboratory measurements of seismo-magnetic conversions in fluid-filled Fontainebleau sand,” Geophysical Research Letters, vol. 33, no. 1, Article ID L01302, 2006.
[4]  R. Chandler, “Transient streaming potential measurements on fluid-saturated porous structures: an experimental verification of biot's slow wave in the quasi-static limit,” Journal of the Acoustical Society of America, vol. 70, no. 1, pp. 116–121, 1981.
[5]  P. M. Reppert and F. D. Morgan, “Streaming potential collection and data processing techniques,” Journal of Colloid and Interface Science, vol. 233, no. 2, pp. 348–355, 2001.
[6]  R. G. Packard, “Streaming potentials across glass capillaries for sinusoidal pressure,” The Journal of Chemical Physics, vol. 21, no. 2, pp. 303–307, 1953.
[7]  C. E. Cooke, “Study of electrokinetic effects using sinusoidal pressure and voltage,” The Journal of Chemical Physics, vol. 23, no. 12, pp. 2299–2303, 1955.
[8]  A. R. Sears and J. N. Groves, “The use of oscillating laminar flow streaming potential measurements to determine the zeta potential of a capillary surface,” Journal of Colloid and Interface Science, vol. 65, no. 3, pp. 479–482, 1978.
[9]  P. M. Reppert, F. D. Morgan, D. P. Lesmes, and L. Jouniaux, “Frequency-dependent streaming potentials,” Journal of Colloid and Interface Science, vol. 234, no. 1, pp. 194–203, 2001.
[10]  P. M. Reppert, Electrokinetics in the earth, Ph.D. thesis, Massachusetts Institute of Technology, 2000.
[11]  E. Tardif, P. W.J. Glover, and J. Ruel, “Frequency-dependent streaming potential of Ottawa sand,” Journal of Geophysical Research B, vol. 116, no. 4, Article ID B04206, 2011.
[12]  P. W. J. Glover and E. Walker, “A grain-size to effective pore-size transformation derived from electrokinetic theory,” Geophysics, vol. 74, no. 1, pp. E17–E29, 2009.
[13]  F. D. Morgan, E. R. Williams, and T. R. Madden, “Streaming potential properties of Westerly granite with applications,” Journal of Geophysical Research B, vol. 94, no. 9, pp. 12449–12461, 1989.
[14]  P. M. Reppert and F. D. Morgan, “Temperature-dependent streaming potentials: 1. Theory,” Journal of Geophysical Research B, vol. 108, no. 11, pp. 3–12, 2003.
[15]  P. M. Reppert and F. D. Morgan, “Temperature-dependent streaming potentials: 2. Laboratory,” Journal of Geophysical Research B, vol. 108, no. 11, pp. 4–13, 2003.
[16]  P. W. J. Glover, E. Walker, and M. D. Jackson, “Streaming-potential coefficient of reservoir rock: A theoretical model,” Geophysics, vol. 77, no. 2, pp. D17–D43, 2012.
[17]  P. W. J. Glover and N. Déry, “Streaming potential coupling coefficient of quartz glass bead packs: dependence on grain diameter, pore size, and pore throat radius,” Geophysics, vol. 75, no. 6, pp. F225–F241, 2010.
[18]  D. L. Johnson, J. Koplik, and R. Dashen, “Theory of dynamic permeability and tortuosity in fluid-saturated porous media,” Journal of Fluid Mechanics, vol. 176, pp. 379–402, 1987.
[19]  E. Walker and P. W. J. Glover, “Characteristic pore size, permeability and the electrokinetic coupling coefficient transition frequency in porous media,” Geophysics, vol. 75, no. 6, pp. E235–E246, 2010.
[20]  A. Revil and L. M. Cathles III, “Permeability of shaly sands,” Water Resources Research, vol. 35, no. 3, pp. 651–662, 1999.
[21]  A. Revil, P. A. Pezard, and P. W. J. Glover, “Streaming potential in porous media 1. Theory of the zeta potential,” Journal of Geophysical Research B, vol. 104, no. 9, pp. 20021–20031, 1999.
[22]  W. T. Thomson and M. D. Dahleh, Theory of Vibration with Applications, Prentice Hall, 1998.
[23]  S. Pride, “Governing equations for the coupled electromagnetics and acoustics of porous media,” Physical Review B, vol. 50, no. 21, pp. 15678–15696, 1994.
[24]  E. Charlaix, A. P. Kushnick, and J. P. Stokes, “Experimental study of dynamic permeability in porous media,” Physical Review Letters, vol. 61, no. 14, pp. 1595–1598, 1988.
[25]  P. W. J. Glover and E. Walker, “Modelling the frequency dependence of hydraulic flow and streaming potential coupling coefficients in capillary bundles and porous rocks,” in Proceedings of the Annual Congress of European Geosciences Union, paper A-02892, Vienna, Austria7, April 2008.
[26]  P. W. J. Glover, I. I. Zadjali, and K. A. Frew, “Permeability prediction from MICP and NMR data using an electrokinetic approach,” Geophysics, vol. 71, no. 4, pp. F49–F60, 2006.
[27]  S. N. Lvov and R. H. Wood, “Equation of state of aqueous NaCl solutions over a wide range of temperatures, pressures and concentrations,” Fluid Phase Equilibria, vol. 60, no. 3, pp. 273–287, 1990.
[28]  S.L. Phillips, H. Ozbek, and R.J. Otto, “Basic energy properties of electrolytic solutions database,” in Proceedings of the 6th International CODATA Conference, Santa Flavia, Italy, May 1978, http://www.osti.gov/bridge/purl.cover.jsp;jsessionid =3954E775156A8BC0FA35DB5CE5B402D4?purl=/6269880-iPJPhB/.
[29]  P. N. Sen and P. A. Goode, “Influence of temperature on electrical conductivity on shaly sands,” Geophysics, vol. 57, no. 1, pp. 89–96, 1992.
[30]  P. Leroy, A. Revil, A. Kemna, P. Cosenza, and A. Ghorbani, “Complex conductivity of water-saturated packs of glass beads,” Journal of Colloid and Interface Science, vol. 321, no. 1, pp. 103–117, 2008.
[31]  M. Z. Jaafar, J. Vinogradov, and M. D. Jackson, “Measurement of streaming potential coupling coefficient in sandstones saturated with high salinity NaCl brine,” Geophysical Research Letters, vol. 36, no. 21, Article ID L21306, 2009.
[32]  J. Vinogradov, M. Z. Jaafar, and M. D. Jackson, “Measurement of streaming potential coupling coefficient in sandstones saturated with natural and artificial brines at high salinity,” Journal of Geophysical Research B, vol. 115, no. 12, Article ID B12204, 2010.
[33]  P. W. J. Glover, “What is the cementation exponent? A new interpretation,” The Leading Edge, vol. 28, no. 1, pp. 82–85, 2009.
[34]  P. W. J. Glover, “A generalized Archie's law for n phases,” Geophysics, vol. 75, no. 6, pp. E247–E265, 2010.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133